Notation Reference

a₀ — the floor (transition) acceleration. a₀ = αcH₀/(2π).

α — the apex-symmetry correction factor. α = 2 ln(sec(½) + tan(½)) ≈ 1.0445. Derived from the S² dipole flux conservation. Not the fine-structure constant.

H₀ — the Hubble parameter; the cosmological fold rate; the angular rate of one closure cycle (AP20).

Rₕ — the Hubble radius, Rₕ = c/H₀. The maximum extent of any closing field line.

κ, κ_min, κ₂ — curvature: κ the field-line curvature (a = v²κ); κ_min = 1/Rₕ the minimum (widest-line) curvature; κ₂ = 1/(2Rₕ²) the quadratic coefficient of the tension profile.

τ, T_loop, f_coh — the coherence time τ = 1/H₀; the loop period T_loop = 2π/H₀; the coherent fraction f_coh = τ/T_loop = 1/(2π).

ℳ, ·, μ — the record monoid (ℳ, ·) and its additive measure μ: ℳ → ℝ₊ (Lemma 1).

ℒ, 𝒫, σ — the two sectors and the involution σ of Axiom S connecting them.

ε, ν(ε) — the break and its valuation; ν(ε) = 1, the minimum viable splinter (Axiom B).

T(θ), T_apex, Φ — the tension per unit transverse length T(θ) = Φ/(2πRₕ sinθ); T_apex its apex value; Φ the (conserved) flux.

θ, φ — the colatitude θ from the source pole; φ = π/2 − θ the latitude near the apex.

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the420code.org

Series The 420 Code

Catalogue Ø Artist’s Proofs

Proof Number AP18

Title The Floor

Subtitle Acceleration Scale

Medium Astrophysics / Physics

Artist G

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